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Lung cancer is a leading cause of cancer mortality globally, highlighting theimportance of understanding its mortality risks to design effectivepatient-centered therapies. The National Lung Screening Trial (NLST) employedcomputed tomography texture analysis, which provides objective measurements oftexture patterns on CT scans, to quantify the mortality risks of lung cancerpatients. Partially linear Cox models have gained popularity for survivalanalysis by dissecting the hazard function into parametric and nonparametriccomponents, allowing for the effective incorporation of both well-establishedrisk factors (such as age and clinical variables) and emerging risk factors(e.g., image features) within a unified framework. However, when the dimensionof parametric components exceeds the sample size, the task of model fittingbecomes formidable, while nonparametric modeling grapples with the curse ofdimensionality. We propose a novel Penalized Deep Partially Linear Cox Model(Penalized DPLC), which incorporates the SCAD penalty to select importanttexture features and employs a deep neural network to estimate thenonparametric component of the model. We prove the convergence and asymptoticproperties of the estimator and compare it to other methods through extensivesimulation studies, evaluating its performance in risk prediction and featureselection. The proposed method is applied to the NLST study dataset to uncoverthe effects of key clinical and imaging risk factors on patients' survival. Ourfindings provide valuable insights into the relationship between these factorsand survival outcomes.

Penalized Deep Partially Linear Cox Models with Application to CT Scans of Lung Cancer Patients